Question

Verify Euler's formula for : (a) Cube (b) Cubiod (c) Triangular prism (d) Pentagonal pyramid.

Answer 1

Answer:

Eulers formula is F+V-E=2

for cube

Answer: V - E + F = 2; or, in words: the number of vertices, minus the number of edges, plus the number of faces, is equal to two. ... V - E + F = 12 - 30 + 20 = 32 - 30 = 2, as we expected. Euler's formula is true for the cube and the icosahedron

Step-by-step explanation:

for cuboid

By Euler's formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula F + V = E + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges.

for triangular prism

Recall the Euler's formula, F + V = E + 2 Here number of faces, F = 5 Number of vertices, V = 6 Number of edges, E = 9 Consider, F+V = 5 + 6 = 11 E + 2 = 9 + 2 = 11Hence F + V = E + 2 Thus Euler's formula is verified.

for pentagonal pyramid

If a polyhedron is having number of faces as F, number of edges as E and the number of vertices as V, then the relationship F + V = E + 2 is known as Euler's formula. Following figure is a solid pentagonal prism. Which is true, the Euler's formula is verified.

Answer 2

Step-by-step explanation:

Eulers formula is F+V-E=2

for cube

Answer: V - E + F = 2; or, in words: the number of vertices, minus the number of edges, plus the number of faces, is equal to two. ... V - E + F = 12 - 30 + 20 = 32 - 30 = 2, as we expected. Euler's formula is true for the cube and the icosahedron

Step-by-step explanation:

for cuboid

By Euler's formula the numbers of faces F, of vertices V, and of edges E of any convex polyhedron are related by the formula F + V = E + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges.

for triangular prism

Recall the Euler's formula, F + V = E + 2 Here number of faces, F = 5 Number of vertices, V = 6 Number of edges, E = 9 Consider, F+V = 5 + 6 = 11 E + 2 = 9 + 2 = 11Hence F + V = E + 2 Thus Euler's formula is verified.

for pentagonal pyramid

If a polyhedron is having number of faces as F, number of edges as E and the number of vertices as V, then the relationship F + V = E + 2 is known as Euler's formula. Following figure is a solid pentagonal prism. Which is true, the Euler's formula is verified.